In the Aufbau principle, electrons are filled subshells in increasing order of energy, like 1s is filled before 2s. The value of (n+ℓ) is 1 for 1s and 2 for 2s, therefore, 1s is filled first. But the Aufbau principle is unable to work for three orbitals of 2p ( 2p_{x}_{, }2p_{y, }2p_{z). }These three orbitals (2p_{x}_{, }2p_{y, }2p_{z} ) have the same energy (so-called degenerate orbitals) and the coming electron can be filled in any one of these orbitals. Filling electrons in these orbitals is governed by Hund’s rule of maximum multiplicity. German physicist Friedrich Hund formulated his famous Hund rule around 1927.

## Definition of Hund’s Rule

According to Hund’s rule of maximum multiplicity;

- Every orbital in a subshell is first singly occupied before it is doubly occupied.
- All the electrons in singly occupied orbitals have the same spin (either clockwise or anti-clockwise).

If orbitals of the same energy are available and there are more than one electrons to be filled in these orbitals, each orbital gets one electron. Moreover, if all the orbitals are first singly occupied then these singly occupied orbitals are doubly occupied with upcoming electrons (with opposite spins).

### Diagram of Degeneracy

Hund’s rule for degenerate orbitals of p;

Hund’s rule for degenerate orbitals of d;

**Importance of Hund’s Rule**

If electrons are filled according to Hund’s rule, it lowers the energy of the system and makes it more stable. A more stable system is less reactive. Look at the case of Nitrogen.

_{7}N = 1s^{2} , 2s^{2}^{,} 2p^{3}

Ground state electronic configuration of nitrogen shows that the first 4 electrons are filled in 1s and 2s respectively. For the remaining 3 electrons to be filled in 2p_{x}_{, }2p_{y, }and 2p_{z }orbitals there are three different probabilities.

Probability 1: Energy profile diagram

Probability 2: Energy profile diagram

Probability 3: Energy profile diagram

Energy profile diagrams show that electrons filled in separate orbitals with the same spin are more stable with minimum energy as shown in the 3rd probability diagram.

In 1st probability diagram, two electrons are paired up in 2p_{x}, although an empty 2p_{z } orbital is available. As a result energy of the system is raised and it becomes energetically unfavorable.

Similarly, in the 2nd probability diagram, the spin of one electron in one of the singly occupied orbital 2p_{x }/ 2py / 2pz is opposite as compared to the other 2 orbitals. As a result energy of the system increases and makes it energetically unfavorable.

### Convention of Electronic Direction(s)

Conventionally, electrons in singly occupied orbitals are represented with an upward arrow (↑). However, they can also be represented with a downward arrow (↓). There will be no increase or decrease in the energy of a system if all singly occupied electrons are represented with uni-directional arrows (whether upward or downward).

## Examples of Hund’s Rule

### Example no. 1 (Carbon)

_{6}C = 1s^{2}, 2s^{2}, 2p_{x}^{1}, 2p_{y}^{1}, 2p_{z}

Remember that one of the electrons from 2s^{2 } can’t be prompted to empty 2p_{z }because of two reasons:

- Hund’s rule only deals with ground-state electronic configurations.
- The energy of 2s and 2p
_{z }is not the same. The energy of 2s is lesser than the energy of 2p_{z.}This energy gap doesn’t allow the promotion of electrons from 2s to 2p_{z}.

### Example no. 2 (Oxygen)

_{8}O = 1s^{2}, 2s^{2}, 2p_{x}^{2}, 2p_{y}^{1}, 2p_{z}^{1}

In the case of oxygen, four electrons in 2p_{x}_{, }2p_{y, }and 2p_{z} orbitals are first singly occupied with the same spins, and the last electron is paired in any one of the half-filled orbitals but with opposite spin.

### Example no. 3 (Fluorine)

_{9}F = 1s^{2}, 2s^{2}, 2p_{x}^{2}, 2p_{y}^{2}, 2p_{z}^{1 }

In fluorine, there are five electrons to be filled in 2p_{x}_{, }2p_{y, }and 2p_{z} orbitals. First of all three electrons are singly occupied in 2px_{, }2p_{y, }and 2p_{z} orbitals with the same spins. The remaining two electrons are then paired in any of two half-filled orbitals with opposite spins.

### Example no. 4 (Neon)

_{10}Ne = 1s^{2}, 2s^{2}, 2p_{x}^{2}, 2p_{y}^{2}, 2p_{z}^{2}

### Further Examples

**Chromium**

_{24}Cr = [Ar], (3d_{xy })^{1}, (3d_{yz})^{1}, (3d_{zx})^{1}, (3d_{x2 – y2 })^{1}, (3d_{z2 })^{1}, 4s^{1}

**Manganese**

_{25}Mn = [Ar], (3d_{xy })^{1}, (3d_{yz})^{1}, (3d_{zx})^{1}, (3d_{x2 – y2 })^{1}, (3d_{z2 })^{1}, 4s^{2}

**Copper**

_{29}Cu = [Ar], (3d_{xy })^{2}, (3d_{yz})^{2}, (3d_{zx})^{2}, (3d_{x2 – y2 })^{2}, (3d_{z2 })^{2}, 4s^{1}

**Zinc**

_{30}Zn =[Ar], (3d_{xy })^{2} , (3d_{yz})^{2} , (3d_{zx})^{2} , (3d_{x2 – y2 })^{2}^{ }, (3d_{z2 })^{2 }, 4s^{2}

## Concepts Berg

**Why does Hund’s rule hold?**

Hund‘s rule holds because electrons prefer to fill orbitals with the same spin first, before pairing off with opposite spins. It’s all about low energy and stability.

**How do you draw Hund’s rule? **

Hund’s rule can be drawn by showing electrons in the degenerate orbitals with arrows pointing in the same direction, indicating that they have parallel spins. Any further electrons are shown pointing in the opposite direction, indicating that electrons have paired with opposite spins.

**Why is Hund’s rule called the law of maximum multiplicity? **

Hund‘s rule is called the law of maximum multiplicity because it states that the electrons in an atom will occupy an orbital such that the total spin multiplicity is maximized. This means that, in an atom, the electrons will fill orbitals in such a way that the total spin (which is related to the total number of unpaired electrons in the atom) is maximized. The maximum spin multiplicity is achieved when all of the orbitals are singly occupied and all the electrons have the same spin.

**According to Hund s rule, what is the electronic configuration of Fe ^{+2} and Cr^{+3}?**

Fe^{+2} = [Ar], 3d^{6}

Cr^{+3 }= [Ar], 3d^{3}

**Is the Hunds rule followed in Lewis’s structures? **

No, Hund‘s rule is not always followed in drawing Lewis structures. Hund‘s rule states that in a group of indistinguishable electrons, the electrons will occupy all available orbitals of the same energy before any electrons are placed in orbitals of higher energy. This rule is used to determine the most stable arrangement of electrons in an atom, but it is not always followed when drawing a Lewis structure.

**What is the difference between Hund’s rule and the Aufbau principle? **

Hund‘s rule states that electrons in an atom will fill the lowest–energy orbitals first and will occupy the orbitals with the same energy in a parallel spin before pairing. This means that electrons in an atom will fill orbitals of the same energy with a single electron each before pairing. The Aufbau principle states that electrons will fill the lowest energy orbitals first and will fill orbitals of higher energy as the number of electrons increase. This means that electrons will fill orbitals from lowest to highest energy and will not pair until all orbitals of the same energy are filled.

**Reference Books**

- The tenth edition of Chemistry by Zumdahl and DeCoste

**Reference links**

- Glossary (chem.purdue.edu)
- Supplemental_Modules (chem.libretexts.org)
- Definition (chemicool.com)